1. Field of the Invention
The present invention relates to a three-dimensional photonic crystal having a three-dimensional periodic-refractive-index structure and to functional devices, such as a waveguide, a resonator, a filter, a laser, and a polarizing device, including the same.
2. Description of the Related Art
The concept of controlling transmission and reflection characteristics of electromagnetic waves with structures having a size equal to or smaller than the wavelength of the waves has been proposed by Yablonovitch (Physical Review Letters, Vol. 58, p. 2059, 1987). According to this document, transmission and reflection characteristics of electromagnetic waves can be controlled by periodic structures having a period equal to or smaller than the wavelength.
Such a structure is known as a photonic crystal. It has been suggested that photonic crystals can be used to realize a reflective mirror having a reflectance of 100% in a certain wavelength range.
Thus, a certain wavelength range in which a reflectance of 100% can be realized is referred to as a photonic bandgap, by analogy with the energy gap of semiconductors.
In addition, when the structures having a size equal to or smaller than the wavelength have a three-dimensional fine periodic structure, the photonic bandgap can be realized for electromagnetic waves such as light incident from all directions. Hereinafter, this is referred to as a complete photonic bandgap.
When the complete photonic bandgap is realized, various applications, such as a suppression of spontaneous emission in a light-emitting device, can be performed to realize new functional devices. In order to realize a functional device that operates over a wider frequency range, a structure having a wider complete photonic bandgap has been desired.
Some structures exhibiting such a photonic bandgap have been proposed (U.S. Pat. Nos. 5,335,240, 5,440,421, and 6,597,851).
FIG. 18A shows a woodpile structure proposed in U.S. Pat. No. 5,335,240. In this structure, a plurality of columnar structures disposed in parallel are stacked, the alignment of each layer rotated by 90 degrees with respect to that of adjacent layers.
FIG. 18B is a schematic view of a structure exhibiting a photonic bandgap disclosed in U.S. Pat. No. 5,440,421. In this structure, a plurality of holes have been made in a direction perpendicular to a plurality of columnar structures that are disposed in parallel so that parts of the columnar structures overlap in the stacking direction.
FIG. 18C is a schematic view of a structure exhibiting a photonic bandgap disclosed in U.S. Pat. No. 6,597,851. In this structure, layers having holes provided in the form of a triangular lattice and columnar structures provided in the form of a triangular lattice are stacked with a shift of ⅓ of the fundamental period between adjacent layers.
In the woodpile structure disclosed in U.S. Pat. No. 5,335,240, since four layers constitute one period, the structure is simple and is easily produced. However, the structure has a strong anisotropy, resulting in a strong directional dependence of the photonic bandgap.
The structure disclosed in U.S. Pat. No. 5,440,421 also has a complete photonic bandgap. However, a plurality of very deep holes must be formed, and it is very difficult to produce the structure.
The structure disclosed in U.S. Pat. No. 6,597,851 has an anisotropy smaller than that of the woodpile structure and has a relatively large photonic bandgap. However, since six layers constitute one period, the fabrication process is complex, for example, high accuracy is necessary for the alignment of layers. Thus, it is difficult to produce the structure.